The one thing the government should not do in the current circumstances is accede to the demands of the banks to alter the conditions of the bail-out plan announced earlier this week. Their attempt to change the terms of the deal in order to pay dividends to their shareholders – which they would only be able to do off the back of money pumped in by the taxpayer – is a recipe for shoving public money into the banks through one door and then passing it out through another door straight into the hands of the shareholders. It is breathtaking in its sheer arrogance and cheek.

In fact, there is a case for making changes to what the government announced – but in the direction of strengthening the position of the government and taxpayer, not further weakening it.

The government is quite right to intervene into the financial situation rather than stand idly by. The problem is that, in its current form, the package exposes the public sector to considerable risk. This, and not the unacceptable demands of the banks, is what the government should now address.

When the government sold off the nationalised industries, there was a bit of small print that was mostly ignored in the stampede. Share prices can go down as well as up. The BBC's Nick Robinson revived this point in his news reports on Monday. He was right to do so. The FTSE 100 index lost more than 7% on Wednesday, reportedly its fifth biggest percentage fall in history; and it is heading sharply down again. Too much of the response to the government's plan assumes that the price of shares in the affected banks will rise sufficiently for the taxpayer to avoid making losses. This is a very big assumption.

The Financial Times report of the banks' share prices on Tuesday, the day after the bank bail-out was announced, showed the nature of the risks to taxpayers: "Shares in HBOS slumped 27% to 90p, 23.6p below the price at which the government has committed to invest £8.5bn, while Lloyds TSB shares fell more than 14% to 162p, 11.3p below the price at which it is placing shares with the government. RBS shares, which dropped 8%, closed at 65.7p – just above the placing price of 65.5p." This would have meant losses of over £2bn for the taxpayer.

If the shares of these banks fall below the purchase price, the taxpayer loses. If the injection of government capital raises the banks' share prices, it won't necessarily do so by more than the purchase price. So, existing shareholders could sell at prices above their market value, but the government would be unable to sell its stake and would still have lost out. Under these arrangements, the risk has effectively been placed onto us, the public, rather than on the shareholders of RBS, HBOS and Lloyds TSB. This is why the pressure from these banks to change the terms of the government's deal is so utterly outrageous, and why, when Alastair Darling said on Newsnight on Wednesday evening that he would not "put billions into banks only to see it disappear out of the door", we must hope he sticks to his guns.

In fact, by raising the question of the shareholder dividends, the banks have brought the basic elements of the bail-out back onto the agenda. The pressure should go the other way – the banks may believe that the deal is too punishing, whereas it is the taxpayer who deserves greater protection. As Ken Livingstone argues, the government must not pay money for shares that may be considerably overpriced or even worthless.

The government should, instead, announce it is ready to take over the functioning of any of the banks that turn out to have no value for shareholders: depositors should be guaranteed, but not shareholders. The loss would, then, have been borne by RBS, HBOS or Lloyd's TSB shareholders, but losses would have been focused on them and not on the taxpayer.

Earlier this week, a ComRes Newsnight poll found the public blame bankers and speculators most for the current crisis – 37% blaming the banking industry and 21% blaming the speculators. On the basis of the banks' latest unacceptable attempt to extract greater gain for their shareholders from the government's bail-out scheme, public opinion is unlikely to change.